Hmm tough one.....this could be a lot of extra stress just when you don't need it. My DD has a little dog, I crate my dogs when she comes over, they are reasonably fine with small dogs, but not one that will get in their faces, not respect a dog on his bed, etc. They just get annoyed.....DD has in the past agreed to dog sit for me when I was out of town, at night she had her dog in the bed room with her, door closed, and my dogs, according to her, started whining and howling. They don't ever do that normally, even though they may or may not sleep in the room with me, but they wanted to be where the little dog was. She finally gave up and went home, visiting my dogs several times a day instead, she could not sleep.....
So, if your mom brings her dog and you have lots of whining and/or howling going on, would she be willing to board it at a place close to you? Or are you going to be stuck for a few weeks with that racket?
Could she maybe hire a dog sitter instead? When I go out of town and neither of my kids can dog sit, I get someone to stay with them from 5pm to 9am, of course for a few weeks that can get costly, maybe you can offer to help pay for that?